No, I have no idea. Safe mode usually only loads Windows drivers and only enough to make the system run. There is nothing you can do to make the drive have bad sectors in or out of safe mode. The only thing I can think of at the moment is that safe mode does not load some of the drivers for the diagnostic program to run correctly.
EDIT: If it concerns you, tell them to put it in their machine and run the diagnostic test. Bad sectors is a physical defect in the drive itself.